{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 异常值的处理方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd \n",
    "import scipy.stats as stats\n",
    "import scipy\n",
    "\n",
    "\n",
    "from datetime import datetime \n",
    "import statsmodels.formula.api as smf  \n",
    "\n",
    "\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt \n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "\n",
    "from matplotlib.font_manager import FontProperties \n",
    "from pylab import mpl\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell \n",
    "\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "\n",
    "pd.set_option('display.max_columns', None)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Money</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-19</th>\n",
       "      <td></td>\n",
       "      <td>96.050</td>\n",
       "      <td>99.980</td>\n",
       "      <td>95.790</td>\n",
       "      <td>99.980</td>\n",
       "      <td>126000.00</td>\n",
       "      <td>4.940000e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>99.98</td>\n",
       "      <td>104.300</td>\n",
       "      <td>104.390</td>\n",
       "      <td>99.980</td>\n",
       "      <td>104.390</td>\n",
       "      <td>19700.00</td>\n",
       "      <td>8.400000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>104.39</td>\n",
       "      <td>109.070</td>\n",
       "      <td>109.130</td>\n",
       "      <td>103.730</td>\n",
       "      <td>109.130</td>\n",
       "      <td>2800.00</td>\n",
       "      <td>1.600000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>109.13</td>\n",
       "      <td>113.570</td>\n",
       "      <td>114.550</td>\n",
       "      <td>109.130</td>\n",
       "      <td>114.550</td>\n",
       "      <td>3200.00</td>\n",
       "      <td>3.100000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>114.55</td>\n",
       "      <td>120.090</td>\n",
       "      <td>120.250</td>\n",
       "      <td>114.550</td>\n",
       "      <td>120.250</td>\n",
       "      <td>1500.00</td>\n",
       "      <td>6.000000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>4776195.45</td>\n",
       "      <td>4.427953e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>5682598.16</td>\n",
       "      <td>5.166981e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>5763192.61</td>\n",
       "      <td>5.246691e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>4922871.63</td>\n",
       "      <td>4.806126e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>11023379.17</td>\n",
       "      <td>1.167773e+08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8251 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close       Volume  \\\n",
       "Day                                                                         \n",
       "1990-12-19              96.050    99.980    95.790    99.980    126000.00   \n",
       "1990-12-20     99.98   104.300   104.390    99.980   104.390     19700.00   \n",
       "1990-12-21    104.39   109.070   109.130   103.730   109.130      2800.00   \n",
       "1990-12-24    109.13   113.570   114.550   109.130   114.550      3200.00   \n",
       "1990-12-25    114.55   120.090   120.250   114.550   120.250      1500.00   \n",
       "...              ...       ...       ...       ...       ...          ...   \n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126   4776195.45   \n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306   5682598.16   \n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953   5763192.61   \n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529   4922871.63   \n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497  11023379.17   \n",
       "\n",
       "                   Money  \n",
       "Day                       \n",
       "1990-12-19  4.940000e+05  \n",
       "1990-12-20  8.400000e+04  \n",
       "1990-12-21  1.600000e+04  \n",
       "1990-12-24  3.100000e+04  \n",
       "1990-12-25  6.000000e+03  \n",
       "...                  ...  \n",
       "2024-09-24  4.427953e+07  \n",
       "2024-09-25  5.166981e+07  \n",
       "2024-09-26  5.246691e+07  \n",
       "2024-09-27  4.806126e+07  \n",
       "2024-09-30  1.167773e+08  \n",
       "\n",
       "[8251 rows x 7 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('datasets/000001.csv')\n",
    "data['Day'] = pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "data.set_index('Day', inplace = True)\n",
    "data.sort_values(by = ['Day'],axis=0, ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Money</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-03</th>\n",
       "      <td>647.870</td>\n",
       "      <td>637.720</td>\n",
       "      <td>647.710</td>\n",
       "      <td>630.530</td>\n",
       "      <td>639.880</td>\n",
       "      <td>23451800.00</td>\n",
       "      <td>1.806930e+08</td>\n",
       "      <td>-0.012333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>639.880</td>\n",
       "      <td>641.900</td>\n",
       "      <td>655.510</td>\n",
       "      <td>638.860</td>\n",
       "      <td>653.810</td>\n",
       "      <td>42222000.00</td>\n",
       "      <td>3.069230e+08</td>\n",
       "      <td>0.021770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>653.810</td>\n",
       "      <td>655.380</td>\n",
       "      <td>657.520</td>\n",
       "      <td>645.810</td>\n",
       "      <td>646.890</td>\n",
       "      <td>43012300.00</td>\n",
       "      <td>3.015330e+08</td>\n",
       "      <td>-0.010584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>646.890</td>\n",
       "      <td>642.750</td>\n",
       "      <td>643.890</td>\n",
       "      <td>636.330</td>\n",
       "      <td>640.760</td>\n",
       "      <td>48748200.00</td>\n",
       "      <td>3.537580e+08</td>\n",
       "      <td>-0.009476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>640.760</td>\n",
       "      <td>637.520</td>\n",
       "      <td>637.550</td>\n",
       "      <td>625.040</td>\n",
       "      <td>626.000</td>\n",
       "      <td>50985100.00</td>\n",
       "      <td>3.985190e+08</td>\n",
       "      <td>-0.023035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>4776195.45</td>\n",
       "      <td>4.427953e+07</td>\n",
       "      <td>0.041547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>5682598.16</td>\n",
       "      <td>5.166981e+07</td>\n",
       "      <td>0.011589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>5763192.61</td>\n",
       "      <td>5.246691e+07</td>\n",
       "      <td>0.036131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>4922871.63</td>\n",
       "      <td>4.806126e+07</td>\n",
       "      <td>0.028850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>11023379.17</td>\n",
       "      <td>1.167773e+08</td>\n",
       "      <td>0.080637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7223 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close       Volume  \\\n",
       "Day                                                                         \n",
       "1995-01-03   647.870   637.720   647.710   630.530   639.880  23451800.00   \n",
       "1995-01-04   639.880   641.900   655.510   638.860   653.810  42222000.00   \n",
       "1995-01-05   653.810   655.380   657.520   645.810   646.890  43012300.00   \n",
       "1995-01-06   646.890   642.750   643.890   636.330   640.760  48748200.00   \n",
       "1995-01-09   640.760   637.520   637.550   625.040   626.000  50985100.00   \n",
       "...              ...       ...       ...       ...       ...          ...   \n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126   4776195.45   \n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306   5682598.16   \n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953   5763192.61   \n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529   4922871.63   \n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497  11023379.17   \n",
       "\n",
       "                   Money  Raw_return  \n",
       "Day                                   \n",
       "1995-01-03  1.806930e+08   -0.012333  \n",
       "1995-01-04  3.069230e+08    0.021770  \n",
       "1995-01-05  3.015330e+08   -0.010584  \n",
       "1995-01-06  3.537580e+08   -0.009476  \n",
       "1995-01-09  3.985190e+08   -0.023035  \n",
       "...                  ...         ...  \n",
       "2024-09-24  4.427953e+07    0.041547  \n",
       "2024-09-25  5.166981e+07    0.011589  \n",
       "2024-09-26  5.246691e+07    0.036131  \n",
       "2024-09-27  4.806126e+07    0.028850  \n",
       "2024-09-30  1.167773e+08    0.080637  \n",
       "\n",
       "[7223 rows x 8 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new = data['1995-01':'2024-09'].copy()\n",
    "data_new['Close'] = pd.to_numeric(data_new['Close'])\n",
    "data_new['Preclose'] = pd.to_numeric(data_new['Preclose'])\n",
    "# 计算000001上证指数日收益率 两种：\n",
    "data_new['Raw_return'] = data_new['Close'] / data_new['Preclose'] - 1\n",
    "data_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data = data_new.resample('ME')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.001466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.025258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.145660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.231358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.001981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.028603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.043575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.022263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.024255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.124383</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-03-31   -0.001466\n",
       "1995-06-30   -0.025258\n",
       "1995-09-30    0.145660\n",
       "1995-12-31   -0.231358\n",
       "1996-03-31    0.001981\n",
       "...                ...\n",
       "2023-09-30   -0.028603\n",
       "2023-12-31   -0.043575\n",
       "2024-03-31    0.022263\n",
       "2024-06-30   -0.024255\n",
       "2024-09-30    0.124383\n",
       "\n",
       "[119 rows x 1 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Quarter_data = data_new.resample('QE')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "Quarter_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.142899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-12-31</th>\n",
       "      <td>0.651425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-12-31</th>\n",
       "      <td>0.302153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-12-31</th>\n",
       "      <td>-0.039695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999-12-31</th>\n",
       "      <td>0.191750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-12-31</th>\n",
       "      <td>0.517277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>-0.206180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>-0.175167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>0.102670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>-0.153997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-31</th>\n",
       "      <td>-0.083253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-12-31</th>\n",
       "      <td>1.304334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-12-31</th>\n",
       "      <td>0.966593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-31</th>\n",
       "      <td>-0.653941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-12-31</th>\n",
       "      <td>0.799825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-12-31</th>\n",
       "      <td>-0.143131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-12-31</th>\n",
       "      <td>-0.216753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31</th>\n",
       "      <td>0.031695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>-0.067493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-31</th>\n",
       "      <td>0.528691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>0.094136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>-0.123062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>0.065578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>-0.245911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-31</th>\n",
       "      <td>0.223032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-31</th>\n",
       "      <td>0.138667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-12-31</th>\n",
       "      <td>0.048001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12-31</th>\n",
       "      <td>-0.151250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.037007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.121536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-12-31   -0.142899\n",
       "1996-12-31    0.651425\n",
       "1997-12-31    0.302153\n",
       "1998-12-31   -0.039695\n",
       "1999-12-31    0.191750\n",
       "2000-12-31    0.517277\n",
       "2001-12-31   -0.206180\n",
       "2002-12-31   -0.175167\n",
       "2003-12-31    0.102670\n",
       "2004-12-31   -0.153997\n",
       "2005-12-31   -0.083253\n",
       "2006-12-31    1.304334\n",
       "2007-12-31    0.966593\n",
       "2008-12-31   -0.653941\n",
       "2009-12-31    0.799825\n",
       "2010-12-31   -0.143131\n",
       "2011-12-31   -0.216753\n",
       "2012-12-31    0.031695\n",
       "2013-12-31   -0.067493\n",
       "2014-12-31    0.528691\n",
       "2015-12-31    0.094136\n",
       "2016-12-31   -0.123062\n",
       "2017-12-31    0.065578\n",
       "2018-12-31   -0.245911\n",
       "2019-12-31    0.223032\n",
       "2020-12-31    0.138667\n",
       "2021-12-31    0.048001\n",
       "2022-12-31   -0.151250\n",
       "2023-12-31   -0.037007\n",
       "2024-12-31    0.121536"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Year_data = data_new.resample('YE')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "Year_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 固定比例法\n",
    "\n",
    "这种方法非常容易理解，我们把上下1%的值重新设置,若大于99%分位数的数值，则将其设置为99%分位数值，若低于1%分位数的数值，则将其重新设置为1%分位数值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2744642236184609"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-0.2463139446677537"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].max()\n",
    "Month_data['2000-01':'2024-09']['Raw_return'].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>0.123242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>0.116990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>0.049948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.020053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>0.031710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>297 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_fix = Month_data['2000-01':'2024-09'].copy()\n",
    "Month_data_fix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>0.123242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>0.116990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>0.049948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.020053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>0.031710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>297 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_fix[Month_data_fix['Raw_return'] > Month_data_fix['Raw_return'].quantile(\n",
    "    0.99)] = Month_data_fix['Raw_return'].quantile(0.99)\n",
    "Month_data_fix[Month_data_fix['Raw_return'] < Month_data_fix['Raw_return'].quantile(\n",
    "    0.01)] = Month_data_fix['Raw_return'].quantile(0.01)\n",
    "Month_data_fix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005530\n",
       "std        0.070834\n",
       "min       -0.246314\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005365\n",
       "std        0.068627\n",
       "min       -0.203684\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.185927\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe().round(8)\n",
    "Month_data_fix['2000-01':'2024-09']['Raw_return'].describe().round(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 均值标准差法\n",
    "\n",
    "这种想法的思路来自正态分布,假设$X \\sim N\\left(\\mu, \\sigma^{2}\\right)$，那么\n",
    "\n",
    "\n",
    "$P(|X-\\mu|>k * \\sigma)= \\begin{cases}0.317, & k=1 \\\\ 0.046, & k=2 \\\\ 0.003, & k=3\\end{cases}$\n",
    "\n",
    "通常把**3倍**标准差之外的值都视为异常值，不过要注意的是样本均值和样本标准差都不是稳健统计量，其计算本身受极值的影响就非常大，所以可能会出现一种情况，那就是我们从数据分布图上能非常明显地看到异常点，但按照上面的计算方法，这个异常点可能仍在均值3倍标准差的范围内。因此按照这种方法剔除掉异常值后,需要重新观察数据的分布情况，看是否仍然存在显著异常点,若存在则继续重复上述步骤寻找异常点."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>0.123242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>0.116990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>0.049948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.020053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>0.031710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
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       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_ms = Month_data['2000-01':'2024-09'].copy()\n",
    "\n",
    "Month_data_ms[Month_data_ms['Raw_return'] >= Month_data_ms['Raw_return'].mean() +\n",
    "         3 * Month_data_ms['Raw_return'].std()] = Month_data_ms['Raw_return'].mean(\n",
    "         ) + 3 * Month_data_ms['Raw_return'].std()\n",
    "\n",
    "Month_data_ms[Month_data_ms['Raw_return'] <= Month_data_ms['Raw_return'].mean() -\n",
    "         3 * Month_data_ms['Raw_return'].std()] = Month_data_ms['Raw_return'].mean(\n",
    "         ) - 3 * Month_data_ms['Raw_return'].std()\n",
    "Month_data_ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005530\n",
       "std        0.070834\n",
       "min       -0.246314\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005593\n",
       "std        0.069359\n",
       "min       -0.205210\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.218032\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe().round(8)\n",
    "Month_data_ms['2000-01':'2024-09']['Raw_return'].describe().round(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MAD法\n",
    "\n",
    "**MAD法**是针对均值标准差方法的改进,把均值和标准差替换成稳健统计量，样本均值用样本中位数代替，样本标准差用样本MAD( median absolute deviation)代替：\n",
    "\n",
    "\\begin{aligned}\n",
    "&\\operatorname{md}=\\operatorname{median}\\left(x_{i}, i=1,2, \\cdots, n\\right) \\\\\n",
    "&\\mathrm{MAD}=\\operatorname{mean}\\left(\\left|x_{i}-\\mathrm{md}\\right|, i=1,2, \\cdots, n\\right)\n",
    "\\end{aligned}\n",
    "\n",
    "一般将偏离中位数3倍以上的数据作为异常值，和均值标淮差法相比，其中位数和MAD不受异常值的影响。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>0.123242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>0.116990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
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       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.020053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>0.031710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.158965</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>297 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.158965\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_median = Month_data['2000-01':'2024-09'].copy()\n",
    "\n",
    "median = np.median(Month_data_median['Raw_return'])\n",
    "MAD = np.mean(abs(Month_data_median['Raw_return'] - median))\n",
    "\n",
    "Month_data_median[Month_data_median['Raw_return'] >= 3 * MAD + median] = 3 * MAD + median\n",
    "Month_data_median[Month_data_median['Raw_return'] <= -3 * MAD + median] = -3 * MAD + median\n",
    "\n",
    "Month_data_median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005530\n",
       "std        0.070834\n",
       "min       -0.246314\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005945\n",
       "std        0.064574\n",
       "min       -0.150058\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.158965\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe().round(8)\n",
    "Month_data_median['2000-01':'2024-09']['Raw_return'].describe().round(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 参数假设检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005529580266316066"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8,4))\n",
    "\n",
    "ax.plot('Raw_return',\n",
    "'.-', \n",
    "color = 'r', \n",
    "label = 'Monthly Return',\n",
    "linewidth = 1, \n",
    "data = Month_data['2000-01':]) \n",
    "ax.set_title(\"China's stock market\") \n",
    "ax.set_ylabel('Return') \n",
    "ax.set_xlabel('Year')\n",
    "\n",
    "\n",
    "plt.axhline(y=0, color='blue', linewidth=2)\n",
    "\n",
    "\n",
    "\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(data_format)\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "\n",
    "plt.legend(loc='upper right',fontsize = 8)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![111](./images/CLwMG.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005529580266316066"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=1.8515511117890133, pvalue=0.06491819809694582, df=356)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Month_data['1995-01':'2024-09']['Raw_return'],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=1.3453254245037998, pvalue=0.17954988199447114, df=296)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Month_data['2000-01':'2024-09']['Raw_return'],0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## Question\n",
    " 样本的均值和计算的Z值或者是t-value符号是否是一致的？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "83.2"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 学生的分数数79 79 79 79 100# 均值是多少\n",
    "data = [79,79,79,79,100]\n",
    "np.mean(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=0.7619047619047625, pvalue=0.4885651283802229, df=4)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "stats.ttest_1samp(data,80)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Solarize_Light2',\n",
       " '_classic_test_patch',\n",
       " '_mpl-gallery',\n",
       " '_mpl-gallery-nogrid',\n",
       " 'bmh',\n",
       " 'classic',\n",
       " 'dark_background',\n",
       " 'fast',\n",
       " 'fivethirtyeight',\n",
       " 'ggplot',\n",
       " 'grayscale',\n",
       " 'seaborn-v0_8',\n",
       " 'seaborn-v0_8-bright',\n",
       " 'seaborn-v0_8-colorblind',\n",
       " 'seaborn-v0_8-dark',\n",
       " 'seaborn-v0_8-dark-palette',\n",
       " 'seaborn-v0_8-darkgrid',\n",
       " 'seaborn-v0_8-deep',\n",
       " 'seaborn-v0_8-muted',\n",
       " 'seaborn-v0_8-notebook',\n",
       " 'seaborn-v0_8-paper',\n",
       " 'seaborn-v0_8-pastel',\n",
       " 'seaborn-v0_8-poster',\n",
       " 'seaborn-v0_8-talk',\n",
       " 'seaborn-v0_8-ticks',\n",
       " 'seaborn-v0_8-white',\n",
       " 'seaborn-v0_8-whitegrid',\n",
       " 'tableau-colorblind10']"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "style.available"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "\n",
    "\n",
    "alpha = 0.05  \n",
    "df = 100  \n",
    "t_crit = stats.t.ppf(1 - alpha / 2, df) \n",
    "\n",
    "x = np.linspace(-4, 4, 1000) \n",
    "y = stats.t.pdf(x, df) plt.figure(figsize=(10, 6)) \n",
    "plt.style.use('ggplot') # 设置风格\n",
    "plt.plot(x, y, label=f't-distribution (df={df})', color='blue') \n",
    "\n",
    "plt.fill_between(x, 0, y, where=(x >= t_crit) | (x <= -t_crit), color='red', alpha=0.7, label='Rejection region')\n",
    "\n",
    "\n",
    "plt.axvline(t_crit, color='red', linestyle='--', label=f'Critical value = {t_crit:.2f}') \n",
    "plt.axvline(-t_crit, color='red', linestyle='--') \n",
    "\n",
    "t_value = 2.1\n",
    "plt.axvline(t_value, color='green', linestyle='-', label=f't-value = {t_value}')\n",
    "\n",
    "\n",
    "plt.title('t-distribution with Rejection Regions and t-value')\n",
    "plt.xlabel('t-value')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.legend()\n",
    "\n",
    "\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "num_trials = 10000  \n",
    "num_samples = 1000  \n",
    "results = []  \n",
    "\n",
    "\n",
    "for _ in range(num_trials):\n",
    " \n",
    "    samples = np.random.binomial(n=1, p=0.5, size=num_samples)\n",
    "    results.append(np.mean(samples)) \n",
    "\n",
    "\n",
    "theoretical_mean = 0.5  \n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(np.arange(1, num_trials + 1), results, label='Sample Mean', color='blue', alpha=0.5)\n",
    "plt.axhline(y=theoretical_mean, color='red', linestyle='--', label='Theoretical Mean (0.5)')\n",
    "plt.title('Law of Large Numbers: Sample Mean vs. Theoretical Mean')\n",
    "plt.xlabel('Number of Trials')\n",
    "plt.ylabel('Sample Mean')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.ylim(0, 1) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "import seaborn as sns\n",
    "\n",
    "\n",
    "num_samples = 1000 \n",
    "num_trials = 1000   \n",
    "sample_means = []   \n",
    "\n",
    "\n",
    "for _ in range(num_trials):\n",
    "    samples = np.random.uniform(low=-1, high=1, size=num_samples)  \n",
    "    sample_means.append(np.mean(samples))  \n",
    "\n",
    "plt.figure(figsize=(12, 6))\n",
    "\n",
    "\n",
    "sns.histplot(sample_means, bins=30, kde=True, color='blue', stat='density', label='Sample Means')\n",
    "\n",
    "\n",
    "mu = np.mean(sample_means)\n",
    "sigma = np.std(sample_means)\n",
    "x = np.linspace(mu - 4*sigma, mu + 4*sigma, 100)\n",
    "plt.plot(x, stats.norm.pdf(x, mu, sigma), color='red', linestyle='--', label='Normal Distribution')\n",
    "\n",
    "\n",
    "plt.title('Demonstration of the Central Limit Theorem')\n",
    "plt.xlabel('Sample Means')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show();"
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